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# Quadratic Lyapunov Functions for Mechanical Systems.

#### *Center for Systems Science, Yale University*, Report Number 8703, March 1987

D. E. Koditschek

Yale University

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Abstract |

The “mechanical systems” define a large and important class of highly nonlinear dynamical equations which, for example, encompasses all robots. In this report it is shown that a strict Lyapunov Function suggested by the simplest examplar of the class - a one degree of freedom linear time invariant dynamical system - may be generalized over the entire class. The report lists a number of standard but useful consequences of this discovery. The analysis suggests that the input-output properties of the entire class of nonlinear systems share many characteristics in common with those of a second order, phase canonical, linear time invariant differential equation. |

BibTeX entry |

@inproceedings{kod-yale-1987-1,
title = {Quadratic Lyapunov Functions for Mechanical Systems.},
author = {D.E. Koditschek},
booktitle = {Center for Systems Science, Yale University},
year = {1987},
month = {March},
} |